Numerical simulation of fluid-structure interaction and vortex induced vibration of the circular and truncated cylinders

Vortex induced vibration is a well-known phenomenon in the engineering applications involving the fluid/structure interaction. Especially, it has been observed in various ocean engineering applications such as offshore risers, deep water bridge piers and oil pipelines. In the flow around bluff bodies such as marine risers, in a specific range of Reynolds numbers, the asymmetric vortex shedding at the bluff body wake results in periodic hydrodynamic forces on the riser and consequently the vortex-induced- vibration. When the vortex shedding frequency is close to the natural frequency of the structure, the cylinder tends to dramatically vibrates in transverse direction which is commonly termed as the "lock-in" phenomenon. Since vortex induced vibration is one of the most important causes of fatigue damage and structural instability in marine risers, exploring efficient ways to reduce or suppress vortex induced vibrations, has attracted the attention of many ocean engineering researchers. In the present study, two-way fluid/structure interaction simulation of vortex induced vibration of the circular and truncated cylinders are conducted. For this purpose, laminar flow around an elastically supported two degree of freedom cylinder (circular or truncated), which can freely vibrate in stream-wise and transverse directions, is considered.

To solve the governing equations of two-dimensional, unsteady and incompressible flow over circular and truncated cylinders, a finite volume technique is employed. Moreover, the rigid body motion equations in stream-wise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinder movement. To calculate the rigid body motion of cylinder and treat the fluid-cylinder interaction, a User-Defined Function is used. In every time step, the temporal variation of hydrodynamic forces (lift and drag) determined by solving the mass and momentum equations are employed as the source terms in rigid body motion equations to compute the velocity and displacement of cylinders. Fluid-structure interaction is handled using the Fluent's moving deforming mesh feature which deforms and remeshes cells during transverse and streamwise motions of the cylinders. The pressure-based solver with first-order implicit unsteady formulation is employed to solve the discretized continuity and momentum equations. The coupling between pressure and velocity fields are handled by using computationally efficient fractional step method along with the non-iterative time-advancement algorithm for time matching strategy in computational fluid dynamics solver. To solve the governing equation for the velocity fields, one needs suitable boundary conditions at the inlet, outlet, lower and upper boundaries, and on the surface of cylinders. A uniform profile of free-stream velocity is used at the inlet. At the outlet, the downstream boundary is located far from the cylinders such that the streamwise gradients for the velocity vectors could safely be set equal to zero. Along the upper and lower boundaries, the y-component velocity is considered to be zero while for the x-component velocity, the gradient in the y-direction is set equal to zero. At the cylinder’ walls, the no-slip condition is imposed on both velocity components.

In order to validate the numerical method used in the study of fluid-structure interaction, the results for the transverse oscillations of the circular cylinder and truncated one (with truncation angle of 45 degrees) at different Reynolds numbers are compared with the results of Kumar et al. (2018). It is noteworthy that the obtained results in the present study are in good agreement with those of Kumar et al. (2018) and the numerical model accurately predicts the maximum amplitude of transverse vibration and the width of the lock-in region. Moreover, the influence of the truncation angle (behind the cylinder) on the vibration suppression of truncated cylinders is evaluated. The results show that as the Reynolds number increases from 80 to 85, the vibration of the truncated cylinders enters the lock-in region and experiences a sharp jump in their transverse displacement. Also, in this region, the truncation angle does not have a significant effect on the transverse vibrations of the cylinders and merely reduces their in-line vibration. However, changing the structural design of the cylinder (making a truncation at the back of the cylinder) has a substantial effect on the vibration reduction in the right half of the synchronization region. At Re = 100 (Reynolds number corresponding to the lock-out region), when the truncation angle increases from zero to 60 degrees, the transverse vibration of the cylinder is reduced by about 66%.

In summary, it is concluded that the significant difference in the oscillation amplitude of the circular and truncated cylinders is in the right half of the lock-in region. When the truncation angle increases, the width of the lock-in region decreases.